Einstein's Special Theory of Relativity was proposed a little over a hundred years back. It remained a bedrock of twentieth century physics right up to Quantum Field Theory. However, the failure over several decades to provide a unified description of Electromagnetism and Gravitation or alternatively, Quantum Theory and General Relativity has finally lead researchers to abandon the differentiable spacetime manifold on which all of the above was based. In the most recent approaches we consider a spacetime that is discretized or is noncommutative. This immediately leads to corrections to the Special Theory of Relativity, more specifically to Lorentz Symmetry. It is quite significant that there are observational indicators, particularly in ultra high energy cosmic rays which suggest that such corrections are indeed there. We examine the whole issue in this paper.